Hello,this is the question i don't know. I founnd out the answer,but if f(x)=2 means having a repeated root,then how can it be that 0<x<2? Is it that i misunderstood the concept of discriminant? Thank you!
[MATH]3x^2-6x+k^2=0[/MATH]
Now, as you surmised, we want to look at the discriminant, because if there is only one root, then the discriminant must be zero:
[MATH](-6)^2-4(3)(k^2)=0[/MATH]
[MATH]3-k^2=0[/MATH]
Given that \(0<k\), what must \(k\) be?
Hi. This is a question that you could answer by using a test value. Pick a value for k that is less than sqrt(3), and see what happens.
EG: Let k = 1
3 - 1 = 0
We see that k = 1 does not work; therefore, k < sqrt(3) cannot be correct.
If you don't mind posting the reason why, I'm curious to learn what you were thinking when you originally wrote, "f(x)=2 means a repeated root". (I like to understand how students think.) Cheers
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